Happy New Year!
Well, after taking a short break for the holidays I'm back on track with a new strange discovery. I noticed that the infinite sum Sum(infinity, n=0) {1/(e^n)} = (1+rt(5))/2, or the golden ratio. (While trying to evaluate the sum with raw computing power on my calculator I noticed that the terms completely stopped growing at around n=80 or so.) I can't seem to come up with any reason that e and the golden ratio would be related, and the constant I reached could be close to the value of the golden ratio simply by coincidence. (This actually seems pretty likely because the when the terms stopped growing the constant was slightly lower than the golden ratio- 1.581976707. {The golden ratio is equal to 1.618033989.})
Any ideas?
1 comment:
To follow up:
I recently purchased the Student version of Mathematica, and i computed the sum to be e/(e-1), or approximately 1.51898. This number, although close to the golden ratio, has no algebraic connection to the golden ratio and is close to it simply by coincidence.
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